In chess, a knight can move either two squares horizontally plus one vertically or two squares vertically plus one horizontall.
a) If a knight starts from one corner of a standard 8*8 chessboard, how many different squares could it reach after
i) one move?
ii) two moves?
iii) three moves?

From the corner, it could only reach 2 squares in the first move. In the center of the board, it can reach 8 different squares. However, in the second move, you have two different starting points, but they don't have the availability of all eight positions due to the edge of the board. Also, since the problem is phrased as "different squares," you cannot include the square(s) it was previously in.